T.H. Thomas (1994)

The mathematical analysis of hydraulic ram-pumps began soon after their invention in the late 18th century. However simple models of adequate accuracy for use by system designers, pump manufacturers, installers and operators are still not available. This paper describes algebraic models of varying complexity for use by system and pump designers and by those involved in training installers and users. It argues that a pump plus drivepipe, rather than pump alone is the natural unit for modelling and for characterising performance in applications literature. Behaviour is shown to depend primarily upon three parameters. The first is λ the ratio of peak drive flow (which depends upon tuning) to the pump's maximum flow with its impulse valve locked open. The second is μ, the ratio of peak drive flow to the 'Joukowski' flow just sufficient to achieve the system delivery head. The third is R, the ratio of delivery head to drive head. The analysis shows some of the trade-offs entailed in tuning, indicates the optimum choice of drivepipe and explains certain forms of malfunction observable in the field. Several 'rules of thumb' are derived. The paper also indicates areas where the greater precision of computer simulation over algebraic modelling is desirable.

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